The Impact of Particle Collisions in an Atom Smasher

How fast are the particles moving with respect to each other in an atom smasher?

Given the velocities of two particles colliding head on at relativistic speeds in an atom smasher, how do we calculate their relative velocity?

Answer:

The relative velocity of the particles in an atom smasher is 0.9156c.

When two particles collide in an atom smasher, their velocities need to be calculated with respect to each other. In this scenario, the first particle is moving at 0.741c to the left, while the second particle is moving at 0.543c to the right, as measured in the lab rest frame.

To determine the relative velocity between the two particles, we can use the formula:

W_x = |u_x - v_x| / (1 - (u_x * v_x / c^2))

Plugging in the values:

u_x = 0.543c (velocity of the second particle)

v_x = -0.741c (velocity of the first particle)

Calculating:

W_x = |0.543c - (-0.741c)| / (1 - (0.543c * (-0.741c) / c^2))

W_x = |0.543c + 0.741c| / (1 + (0.543 * 0.741))

W_x = 1.284c / 1.402363

W_x = 0.9156c

Therefore, the particles in an atom smasher are moving with a relative velocity of 0.9156c with respect to each other.